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Méta-optique nonlinéaire

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Optical metasurfaces are arrays of coupled optical antennas, with sub-λ size and separation. At variance with current optical components, which need propagation distances of several wavelengths to alter the phase front, metasurfaces can mold polarization, amplitude and phase of light at a sub-λ scale. The latter is an intermediate scale between the case where the optical structures are close or larger than λ and the limit case where they are much smaller than it (like in Rayleigh scattering). In such scale, corresponding to resonant Mie scattering, neither diffracted orders propagate nor the medium can be seen as homogeneous (as e.g. in form birefringence).
We aim to establish the foundations of χ(2) metasurfaces for optical wave engineering based on light structuring at sub-λ scale. Non-plasmonic nanophotonics is presently attracting a great deal of interest because the optical response of high-permittivity dielectric nanoparticles in a low-refractive-index medium exhibits negligible dissipation and strong multipolar magnetic resonances in the visible and near-infrared spectral ranges [1]. Several linear optical nanostructures have been fabricated with TiO2, [2,3] Si3N4, Si or Ge, while χ(3) nonlinear optical results have been obtained for the last three years in the silicon-on-insulator platform, mostly with third-harmonic generation (THG) [4]. In this framework, a monolithic AlGaAs-on-insulator platform constitutes an ideal choice for nanophotonics thanks to a few key properties of AlGaAs : a huge non-resonant χ(2) nonlinearity, a large direct bandwidth that can be varied with aluminum concentration becoming two-photon-absorption free in the C-band of optical communications, and the mature technology of heterostructure laser diodes. Until recently, a full development of an AlGaAs platform was hindered by the difficulty of fabricating monolithic shallow waveguides and cavities as in the silicon-on-insulator system, and in particular by the shortcomings of wet selective oxidation of AlGaAs epitaxial layers. The latter, discovered in 1990, results in non-stoichiometric alumina (AlOx) with optical and electrical properties similar to SiO2 [5]. The use of AlOx layers thinner than 100 nm is common in VCSEL technology [6] and also resulted in the demonstration of an AlGaAs guided-wave optical parametric oscillator [7]. However, fabricating high-quality µm-thick AlOx optical substrates is critical because the selective oxidation of AlGaAs layers induces a strong contraction of the oxide. This typically results in high optical losses in integrated photonic devices, due to defects at the interface between AlOx and the adjacent crystal [8].

Fig. 1 Emission spectrum of an AlGaAs-on-AlOx nanoantenna. [11]

In 2017, we have registered a patent on the fabrication procedure of an AlGaAs heterostructure over an AlOx layer, the latter with a sufficient thickness to confine light in the semiconductor heterostructure by total internal reflection and thus behave as an optical substrate [9]. The first related demonstration has been the second harmonic generation (SHG) by a monolithic nanoantenna at 1.55 µm pump wavelength, with a conversion efficiency higher than the record of plasmonic nanoantennas by four orders of magnitude [10-12]. Based on these grounds, we have the ambition of setting a new paradigm of nonlinear meta-optics, with physical and technological breakthroughs in AlGaAs-on-insulator nanophotonics and two well-identified goals : 1) a metasurface implementing beam shaping on the field generated by classical up-conversion ; 2) a metasurface for the quantum-state engineering of signal-idler photon pairs generated by spontaneous parametric down-conversion (SPDC).

The last two years have witnessed a tremendous progress in all-dielectric nonlinear nanophotonics, marking the transition from the study of χ(3) effects to the exploration of χ(2) effects. Not only the latter are intrinsically stronger than the former under similar experimental conditions (e.g. SHG vs. THG in figure 1), but they can also give rise to SPDC and thus pave the way to free-space quantum optics on-chip. The leadership of MPQ in this domain stems from the first SHG demonstration in a single nanoantenna in 2016 (see figure 1), with 10-5 efficiency for a pump of 1.6 GW/cm2 [10,11]. Following this breakthrough, similar results have been obtained by other groups in Australia and US still on single nanoantennas [13,14], within a research field that has quickly become highly competitive. Very recently, MPQ has also reported on the complex polarization features of the SHG field [15] and its dependence on fabrication tolerances [16]. Finally, we have focused our investigations on AlGaAs nano-dimers shown in figure 2 [17], which can be seen as a first step towards the demonstration of a χ(2) metasurface. The latter is a two-dimensional arrangement of a large number of nanoresonators with subwavelength distances, whose nonlinear emissions interfere coherently. Our metasurface, with a mm2 footprint and internal distances around 30 nm, bridge the gap between the nanometer and millimeter scales.

Fig. 2 From AlGaAs pillars to dimers : a) scheme ; b) electron-microscope picture ; and c) zoom on a single dimer.

Our research is original in several respects. First of all, no χ(2) metasurface is available to date. Moreover, the only SPDC preliminary experiment at the nanoscale has been carried out by us on a single nanocylinder [18], and the related physics of a collective quantum state delocalized on a metasurface is still unexplored. In that work [19], we experimentally demonstrated nonlinear AlGaAs nano-disk sources of high-rate heralded photons with non-classical correlations, establishing a quantum-classical correspondence between SPDC and SFG (see figure 3).
Finally, in the last few months we have observed an optically induced, gigantic (up to 60%) and ultra-fast (picosecond) modulation of the SHG from an AlGaAs nanoresonator. In this yet unpublished work, a weak control beam absorbed by a single nanocylinder results in a slight refractive-index change induced by the excess of photo-generated carriers. The latter suffices to cause a change of the resonant mode at the second harmonic and thus a drastic change of the conversion efficiency, insofar the latter is governed by an overlap integral between the interacting fields. We are presently extending this optical control to the case of a metasurface and trying to demonstrate its electric counterpart, where the carrier population is modified by field-induced charge transfer instead of optical absorption.
Let us recall that on-demand generation of arbitrary wavefront is essential for example in advanced micro-manipulation [19], because focused Gaussian beams can provide only limited trapping capabilities since they are severely limited by diffraction. Our metasurface will allow to shape phase and amplitude of light fields to provide diffraction-free light beams like Airy beams. Using the current state-of-the-art of commercial devices, on-demand shaped light can be obtained using spatial light modulators (SLMs). Even though these devices offer a high degree of flexibility for the wavefront generation, they have a high cost, a limited resolution, relatively long (milliseconds) reconfiguration times, and need an additional lens [19].For these reasons, the field of nanoparticle manipulation will enormously benefit from the these dielectric metasurfaces that will provide accurate and fast reconfigurable structured light.

Fig. 3 SPDC generation of heralded photons in a single AlGaAs nanoantenna. [20]

More in general, in recent years metasurfaces have gained enormous momentum because of their promise for ultrathin devices compatible with planar fabrication technology that can potentially replace bulky, diffraction-limited optical components [3]. Many plasmonic metasurfaces with beam bending [20], beam focusing [21], hologram formation [22], and beam shaping [23] capabilities have been developed. While so far wavefront manipulation has been mainly performed in the linear regime, exploiting the huge χ(2) nonlinearity of all-dielectric AlGaAs metasurface will open the way to two crucial options : 1) the generation of background-free shaped light at new frequencies, which can enhance detection and imaging efficiency [24] ; and 2) a drastically improved ultrafast all-optical or electrical control of the generated wavefront. These are decisive advantages with respect to the recent achievements of nonlinear plasmonic metasurfaces, whose 5 order-of-magnitude lower SHG efficiency and huge ohmic losses make them impractical for most applications. Eventually, placing our metasurface on the tip of a fiber will result in a major breakthrough for photonics : background-free, ultrafast, deeply modulated and arbitrary beam shaping at the output end of an endoscope or on a near-field probe.
Besides this purely classical SFG application, our research will enable its non-classical SPDC counterpart : a local source of entangled photons, for applications in quantum imaging and sensing.
To date, on the one hand SPDC-based photon-pair generation mostly relies on bulk nonlinear crystals, but their properties set all the quantum-state features, and their size hinders miniaturization. On the other hand, SPDC-based photon-pair waveguide sources enable independent control of their polarization and wavelength, but only with a limited number of modes. We are convinced that NOMOS metasurfaces will also provide a unique solution for the synthesis of an arbitrary quantum state that is both fully integratable and easily matched to the continuum of free-space radiation modes. Metasurfaces of nonlinear nano-scale light sources of quantum light offer an unexplored potential for highly indistinguishable spatial photonic modes, as well as for spatial multiplexing of several sources of heralded photons.

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